What is Calculus?
Calculus is the branch of mathematics that deals with rates of change and
motion.
Differential calculus is concerned with finding the
instantaneous rate at which one quantity changes with respect to another.
This rate of change is called the derivative of the first quantity with
respect to the second.
Integral calculus deals with the inverse of the
derivative: finding a function when its rate of change is known. Determining
the original function, having been given its derivative, is called
integration, and the function is called the integral.
Without calculus, problems in physics, as well as most other braches of
science, could not be solved.
What is physics?
Physics is the quantitative branch of science dealing
with the nature of matter and energy and the relationship between them.
Classical physics generally refers to pre-twentieth-century concepts such as
mechanics, electricity and magnetism, light and thermodynamics. Modern
physics incorporates the theories of quantum mechanics and relativity, as
well as other theoretical innovations, to explain the nature of our
universe.
Why is Isaac Newton such a prominent figure in the field of physics?
Isaac Newton (1642-1727) is considered one of the
greatest scientists in history. A British Physicist and mathematician, he
formulated the laws of motion, discovered the universal gravitational law,
and developed calculus all before the age of 30.
Why is Albert Einstein such a prominent figure in the field of physics?
Albert Einstein (1879-1955) is considered one of the
greatest scientists of all time. A German born physicist who sparked a
revolution in the ways in which we think about matter and energy. Einstein
constantly challenged traditional scientific assumptions. He is perhaps best
remembered for his theories of special and general relativity (new paradigms
for understanding space and time), and his discovery of the particle nature
of light. His contributions to science, as well as to humanity, have had
profound effects on the modern world.
What is the difference between a scalar and a vector?
A scalar is a number or measure that is not associated
with a direction. The term scalar refers to any quantity that is measurable
on a scale. (Example: a train traveled 10 miles)
A vector is a quantity that has magnitude and direction
(example: a train traveled 10 miles north.)
What are a positive g and a negative g?
Both positive and negative g refer to g-force, which is
really another name for inertia, or an object's tendency to resist change in
speed or direction of motion.
The feel of gravity and g-force are similar sensations.
If you accelerate upward, as you do when an elevator starts rising, a
gravity-like sensation pulls downward and you feel extra heavy (positive g).
As you decelerate when a rising elevator comes to a stop, this gravity like
sensation pushes upward and you feel unusually light (negative g).
What is the difference between weight and mass?
Weight and mass refer to different characteristics of an
object. Weight refers to the force or "pull" of gravity on an
object. This force depends on the object's mass-the quantity of matter
contained in the object.
Weight can be calculated by multiplying an object's mass
m by the gravitational constant g .
Weight = mg
Mass and weight are measured in different units: mass in
kilograms and weight in pounds.
What is the relationship between mass, acceleration, and force?
Acceleration is the time rate of change of velocity. Mass
resists acceleration: the more mass an object has, the less it accelerates.
Force causes acceleration: it is the influence that causes an object to
accelerate. The stronger the force -- the greater the acceleration.
These ideas can be combined into one observation: an
object's force is equal to the product of its mass times the acceleration.
It can also be represented in the formal
F=ma
Where F is force, m is mass and a is acceleration.
What are Newton's three laws of motion?
1. A body at rest stays at rest unless acted upon by a force, and a body in
motion continues to move in a straight line absent an intervening
force.
A book placed on a table stays unless a force moves it,
and an arrow shot in space will continue to fly in a straight line. (On
earth, the arrow's flight is cut short by the forces of gravity and air
resistance).
2. The effect produced on a body by a force depends on the amount of that
force and inversely on the mass of the body.
Throw a baseball twice as hard and it will go twice as
far; throw a baseball weighing half the weight of another baseball with the
same force and the lighter ball will go twice as far as the heavier
one.
3. For every action there is an equal and opposite reaction.
To climb a ladder, you must push down or exert a force on
the rungs. The reaction to this downward thrust is a movement up the
opposite direction.
What is the difference between velocity and acceleration?
Velocity or speed, is a function of the distance an
object travels during a measured amount of time. It is calculated by
dividing distance by time.
Acceleration is the rate of change of velocity with
respect to time. To calculate acceleration, subtract the starting velocity Vs,
from the final velocity, Vf and divide by the time required to
reach the final velocity, t. The formula is:
Acceleration = Vf - VS
t
What is a jerk?
While commonly used as an insult, jerk, in physics,
refers to the rate of change of an object's acceleration. Jerk is the third
derivative of position with respect to time. Velocity, which describes the
change of an object's position with respect to time, and acceleration, the
change in velocity over time, are the first and second derivatives of
position.
What is terminal velocity?
Gravity causes all objects to accelerate downward at a
steady rate of increase. Terminal velocity occurs when a falling object
stops accelerating downward because of its contact with air.
As its falling speed increases, an object encounters a
corresponding increase in upward force from its contact with t he air. When
the speed becomes great enough, the air's upward force of air resistance,
can cancel the downward force or weight of the object. At that point, the
object experiences zero net force and no longer accelerates. Instead, it
descends at a constant downward velocity, its terminal velocity. This
velocity is determined partly by the object's density and size, and partly
by its aerodynamics.
What is the difference between static friction and sliding friction?
Friction is either static or sliding; it is caused by the
contact and collision between tiny projections on opposing surfaces. Static
friction is friction between two surfaces that are pressed together but not
sliding across one another. This friction prevents motion between the
surfaces. An example is your hand holding an apple.
Sliding or dynamic friction is friction between two
surfaces that are moving across one another. Sliding friction creates
thermal energy or heat. Examples are car wheels in a skid, children on a
slide, and skis on snow.
A 250-pound man falls into a crevasse that reaches to the
center of the earth. Assuming he lands intact, how much does he weigh?
Nothing. Gravity is a function of the distance between
the centers of mass of two objects. Since the distance between the man's
center of mass and the earth's center of mass is zero after he falls, the
man would be weightless.
What is escape velocity?
If you throw a ball up in the air, it rises, but then
starts to fall due to the planet's gravity. If you throw the ball hard
enough, it will escape the planet's gravity and keep rising forever. The
speed an object must attain to escape the force of the planet's gravity is
called it's escape velocity.
Escape velocity depends on the mass of the planet and the
distance an object is from the planet's center. If the planet is extremely,
then its gravity is strong and the escape velocity is high. The opposite is
true for a planet with a low mass. Also, escape velocity will be higher
closer to a planet's center and lower as you move away from the center.
The earth's escape velocity, from its surface, is about 25,000mph, and the
moon's is about 5,300mph.
What is gravitation?
Gravitation is the force of attraction that draws all
objects in the universe toward one another. It is the force responsible for
the orbit of planets, the motion of stars, and the movement of galaxies; it
is also the reason why a cup knocked off a table falls to the ground. The
term gravitation refers to this attractive force in general, while the term
gravity usually refers to the earth's gravitational pull.
Newton quantified gravity, stating that every object in the universe
attracts every other object with a force proportional to the product of
their masses and inversely proportional to the square of the distance
between them. The formula used to determine the gravitational force between
two objects is:
F= GMm
r2
F is the gravitational force, G is the gravitational constant (9.8 meters
per second per second), M is the mass of the first object, m is the mass of
the second, and r is the distance between them.
Why are there two tides per day?
The tide is caused mainly be the moon's gravity. The moon
exerts a slightly stronger gravitational force of the earth it is nearest
to, causing the water on that side to bulge outward. Another water bulge
occurs on the opposite side of the earth, since the earth is being pulled by
gravity toward the moon (and away from the water on the far side).
The two bulges move across the earth's surface as it
rotates. We experience the bulges as high tides, while the time between the
bulges is when there are low tides. Most seashores experience two high tides
daily, as the two bulges pass once around the earth per day.
The sun's gravity also contributes
to the tides, but its effects are smaller and serve mostly to increase or
decrease the height of the tides.
What is kinetic energy?
Kinetic energy is the energy of a body related to its motion.
The magnitude of the kinetic energy depends on both the mass and the speed of
the object, and it can be expressed by the following equation:
E = 1 mv2
2
Where E is the kinetic energy, m is the mass of the object, and v2 is
its speed squared (multiplied by itself).
What is torque?
Torque is twisting or spinning force that causes an object to
turn about its axis of rotation. When you twist the top off a jar you exert
torque on the jar and cause it to rate of change in angular velocity. The top of
the jar begins to rotate faster and faster in the direction of your torque.
Similarly, when you spin a toy top, you exert torque so that the top undergoes
an angular acceleration.
What is the relationship between wavelength, frequency, and amplitude?
Wavelength is the distance between two consecutive peaks of
an emitted wave. Frequency corresponds to the number of wavelengths that pass by
a certain point in space in a given amount of time. All electromagnetic waves
travel at the same speed, so, for a given period of time, a greater number of
short wavelength waves will pass by a point in space than will long wavelengths.
This means that shorter waves have a higher frequency that longer ones.
The relationship between wavelength, speed, and frequency is
expressed by the equation: c = If, where c is the speed of a light wave in
meters per second (3x108 meter per second in a vacuum), I is the wavelength in
meters, and f is the wave's frequency in Hertz (cycles per second or Hz).
The amplitude of an electromagnetic wave is the height of the
wave, measured from a point midway between a peak and a trough to the peak of
the next wave.
What is the Doppler effect?
Named after Austrian physicist Christian Johann Doppler, who
first described this principle, the Doppler effect refers to the observed
frequency changes in waves due to a source that is moving toward or away from an
observer, or from an observer moving toward or away from the source. It explains
why, to a person standing at a train station, a train's whistle will rise in
pitch as the train approaches the platform (sound waves are compressed), and
fall in pitch as it moves away (sound waves are elongated). Observers on a
speeding train will hear a similar change in pitch from a factory whistle as
they pass it. This is also the Doppler effect at work.
What is resonance?
In physics, resonance refers to the oscillation of a system
at its natural frequency of vibration when triggered by a stimulus with an
appropriate frequency. A common example of this phenomenon occurs in music. If
you strike a note on a piano that is the same frequency as one of the strings of
a nearby guitar, the string on the guitar will resonate (vibrate), even though
it has not been plucked. Resonance can occur in acoustical systems, electrical
systems, mechanical systems, and on the atomic level.
What is ultrasonic?
Ultrasonic refers to sound vibrations with frequencies above
the range audible to the human ear-above a frequency of 20,000 Hz (cycles per
second). Nocturnal animals, such a bats, use ultrasonic vibrations to guide
their movements in the dark.
Ultrasonic waves are used in sonar and as a diagnostic tool to produce images of
the internal body.
What is the sonic boom?
A plane that flies faster than the speed of sound (760 mph)
travels faster than the sound produced by its jet engines. As a result, the
engine's sound waves lag somewhat behind the plane, spreading out in a conical
shape. Since the plane's sound is " contained" within this
trailing cone, you will not hear the plane although you may see it. When the
cone does reach you, a large amount of sound hits you all as once in a
thunderous clap called a sonic boom. The cone itself is a kind of shock wave,
with an abrupt increase in pressure right at its edge (sound and pressure are
closely related).
Note that the sonic boom occurs when the plane's shock wave
reaches your ears, not when the plane breaks the sound barrier.
How is light emitted?
Light is emitted by electrons circling the nucleus of an
atom. The electrons, circling the nucleus in specific patterns called orbitals,
possess a quantity of energy at a given instant of time. Those circling in
orbitals closest to a nucleus have less energy than those in the outer orbitals.
The amount of energy associated with each orbital is called an energy level. If
an electron in a lower energy level gains enough energy, it will jump to a
higher level. When this happens, the electron is said to be
'excited."
As an excited electron moves, it eventually loses energy and
falls back to a lower orbital. The energy an electron releases is equal to the
difference between the energy levels of the higher or lower orbitals. It is this
quantum of released energy, in the form of a photon that we see as emitted
light.
Why do some things glow in the dark?
Substances that glow in the dark store the energy they get
from visible light. This stored energy is gradually released and converted back
into light, which causes the substances to glow dimly.
On a molecular level, the energy from the light excites electrons, which then
become trapped in a high-energy state. It takes a long time for the electrons to
return to their original states, but they are able to "calm down" by
emitting light. Eventually, the electrons will return to their original state
and the glow will fade.
What distinguishes ultraviolet light from infrared light?
The human eye can perceive only a tiny fraction of the
electromagnetic spectrum (the entire range of electromagnetic radiation
classified according to wavelength). The portion that can be seen by humans is
called "visible light." Just above visible light on the spectrum is
ultraviolet light, which has a shorter wavelength, and thus a higher frequency
than visible light. Infrared light exists just below visible light on the
spectrum, and it has a lower frequency, and thus a longer wavelength, than
visible light.
Ultraviolet rays are sometimes used in the treatment of skin
conditions, and they are also used to kill bacteria and sterilize utensils.
Infrared rays can be applied in the treatment of sports-related injuries due to
their ability to warm muscles.
What is polarized light?
Polarization refers to the orientation of the electric field
in an electromagnetic wave. A wave whose electric field is oscillating in the
vertical direction is said to be vertically polarized. Such waves interact with
matter differently than waves polarized in the horizontal direction.
The electric field of light waves from the sun vibrates in
all directions, so direct sunlight is called unpolarized - though, in truth, the
light e see is partially polarized by the earths atmosphere. Polaroid sunglasses
are able to block light that is horizontally polarized and therefore reduce
glare from polarized sunlight reflecting off surfaces.
What is a mirage?
A mirage is an optical phenomenon. Mirages can be divided
into two groups: inferior and superior. An inferior mirage occurs when a layer
of air close to the ground is heated more than the air above it. Light rays
reflecting off the ground must then pass through two layers of air of varying
temperature and density; a hot and relatively low - density layer and a
relatively cool, high - density layer. The boundary between these two layers
produces a lens-like effect, causing the light from the ground to be refracted
(bent). An example of an inferior mirage is what happens on a paved road in the
heat of the summer sun; you see what appears to be a river of water running over
the road.
A superior mirage forms when a layer of air next to the ground is much cooler
that the air above it. Light rays from an object are refracted such a way that
an object appears to be suspended in air above its actual position. This
phenomenon is sometimes referred to as "looming".
Why is "c" the symbol for the speed of light?
The symbol "c" has been used universally to
represent the speed of light (in a vacuum) since the early twentieth century.
Einstein used other symbols, such as "V", in his early relativity
papers, but most books on relativity used C.
The symbol most likely comes from the first letter of the
Latin word celeritas, meaning "swift". The English word celerity, a
rare synonym for speed, as well as the words accelerate and decelerate are
derivatives from the same Latin root.
How can light be redirected?
Light can be redirected in three ways: reflection,
refraction, or diffraction. Reflection occurs when light bounces off a surface
like a mirror. Refraction refers to the bending of light as it passes through
different media. Diffraction is a change in the direction and intensity of a
group of waves after passing by an obstacle or through an aperture (opening).
What is the difference between radar and sonar?
Radar is an acronym for "radio detecting and
ranging." Radar works by scanning surrounding space using high-frequency r
radio waves. These radio waves are sent out from a transmitter and are bounced
back toward the transmitter by the first object they encounter in their path.
The reflected beam is then picked up by a receiver. The strength and direction
of the beam gives information as to the size, distance, altitude, etc., of the
object.
Sonar is an acronym for "sound navigation and ranging". Sonar
determines the location of objects based of the reflection of sound waves. It
was originally developed to detect icebergs after the dinking of the Titanic in
1912
What is Charles' Law?
Jacques Charles was an eighteenth century balloonist who
conducted experiments on the relationship between the temperature of a gas and
its corresponding volume. The physical principle bearing his name states that
the volume of a gas equals a constant value, multiplied by its temperature (in
degrees Kelvin). In other words, the volume of a gas is directly proportional to
its temperature. This law is expressed by the equation:
V = kT. V is the volume of the gas, k is the constant, and T is the
temperature.
What is heat?
Heat is related to the motion or vibration of molecules. All
objects contain some quantity of thermal energy, which is the sum of the kinetic
energies (vibration or movement) of its atoms and molecules. The hotter the
object, the more thermal energy or movement is present in its atoms.
What is the Bernoulli effect?
Circa 1730, Daniel Bernoulli, Swiss mathematician, was first
to describe the Bernoulli effect. Bernoulli discovered that the faster fluid
(defined as anything that flows, such as air, water, or a gas) moves over a
surface, the less pressure it exerts on that surface. If the total energy in a
steadily flowing system is constant along the flow path, then an increase in the
fluid's speed must be matched by a decrease in its pressure.
A common example of the Bernoulli effect in action is the flight in an airplane.
An airplane wing is designed to permit air to flow more rapidly over its upper
surface than over its lower surface; thus the pressure on the top of the wing is
lower than on the bottom. This pressure difference provides the lift that
sustains the plane in flight.
What is a British thermal unit (Btu)?
A Btu is a unit of heat energy. It is the amount of heat
required to raise the temperature of one pound of water from 60°F to 61°F at a
constant pressure.
What is radioactivity?
Radiation includes all forms of energy that travel through
space as rays. Radioactivity, however, is the spontaneous breakup or decay of
certain kinds of heavy atomic nuclei. This breakup is accompanied by the
emission of particles and energy. The energy (or radiation) emitted by these
unstable nuclei are capable of ionizing atoms or molecules, causing them to gain
or lose electrons and take on positive or negative charge. Radiation's impact on
molecules such as DNA makes this form of energy a biological hazard in the case
of prolonged or intense exposure.
What is the difference between nuclear fusion and nuclear fissions?
In fusion, nuclei collide so fast that they stick together
and emit a great deal of energy. This process occurs, for instance, when
lightweight hydrogen nuclei combine to form the somewhat heavier nuclei of
helium. Nuclear fissions occurs when the nuclei of very heavy atoms (such as
uranium and plutonium) capture neutrons and become unstable. They break apart
into nearly equal parts (usually barium and krypton) releasing energy as they
decay.
What was the Manhattan Project?
The Manhattan Project was the code name for the effort to
build the first atomic bomb in the United States during World War II. Many of
the most notable quantum physicists of the day were involved in this project,
including Robert Oppenheimer, Richard Feynman, and Enrico Fermi.
What is the Heidelberg uncertainty principle?
A theory formulated by German physicist Werner Heisenberg in
1927, the uncertainty principal states that it is impossible to know
complementary parameters simultaneously, such s the position and momentum of a
particle (photon, electron, proton, positron, etc.) with perfect accuracy.
Furthermore, the principal states that as one parameter is measured more
accurately, the other one will become less precise.
What is antimatter?
Antimatter consists of elementary particles that have the
mass of ordinary particles - such as electrons, protons, or neutrons-but
opposite electric charges. These antiparticles are called positrons,
antiprotons, and antineutrons.
What is the black hole?
Black holes are cosmic bodies of extremely intense gravity
from which nothing, not even light, can escape. They are formed when matter
undergoes extreme compression, such as during the death of a massive star. When
such a star has used up its internal fuel supply, it becomes unstable and
collapses inward upon itself. The crushing weight of matter falling in from all
sides compresses the dying star to a point of zero volume and infinite density,
which is called a singularity.
What is a wormhole?
A wormhole is a distortion in space-time that acts like a
"tunnel" or "passageway", connecting two distant points in
the universe. Suppose you wanted to travel to the nearest star. It would
normally take more than four years, traveling at the speed of light, to reach
it. But if there was a wormhole connecting the star and your front porch, you
could walk to the star in a few steps.
While worm holes do not violate any known laws of physics,
scientist think that these phenomenas, if they existed, would require
unrealistic amounts of negative energy-a bizarre state of matter that has less
than zero energy.
What is a white hole?
A white hole is a theoretical tool that "balances
out" the concept of a black hole; no astronomer has actually observed this
phenomenon. The equations of general relativity are symmetrical, and an
idealized black hole (a region of very dense space from which nothing can
escape) requires a corresponding white hole to keep it balanced in space-time
(space-time refers to the medium in which matter and energy exist). While a
black hole sucks in everything, even light, a white hole spits everything
out.
What is the grandfather paradox?
The grandfather paradox is used to illustrate how time travel
could violate causality (cause and effect). Here's the premise: suppose you
built a time machine and used it to travel seventy years back in time. In
theory, you could then kill your grandfather before he met your grandmother, and
change the course of history,
The paradox is that if your grandfather died before he met
your grandmother, then you would never have been born. But if you were never
born, you could not have gone back in time to prevent your own birth.
What is a superconductor?
Certain materials that display no resistance to the flow of
electric current are called superconductors. They can carry enormous amounts of
current, and the currents can persist for long periods of time (years) without
loss of energy. They are an essential component of particle accelerators, where
powerful electromagnets need extremely large amounts of current.
Superconductivity can only be achieved if the super-conducting material is below
a certain critical temperature. Before 1986, the working temperature for a
superconductor could not exceed 23.2K (-249.8°C), which required the use of
liquid helium, an expensive and inefficient coolant. But due to the research at
several universities, ceramic metal-oxide compounds were found to be
superconductivity at much higher temperatures. Instead of liquid helium, liquid
nitrogen became the preferred coolant.
What is Occam's razor?
Occam's razor is a philosophical rule for choosing between
competing theories. It states that if two theories predict and explain phenomena
to the same degree of accuracy, then the theory that is simpler is more valid.
Moreover, additional aspects of a theory that do not lend it greater
predictability are unnecessary and should be stripped away.
What is the "Big bang" theory?
The Big bang theory proposes that the universe began in an
explosion approximately 10 billion or more years ago, and that it is still
expanding from that cataclysm. Big bang theorists believe that the various
particles of matter today were produced within the first few minutes of the big
bang, when energy and extremely high temperatures formed the elements in the
early universe.
Recent evidence indicates that hydrogen and helium would have been the primary
products of the big bang, with heavier elements, such as oxygen and carbon,
produced later within stars. As the universe expanded, the hydrogen and helium
cooled and condensed into stars and galaxies.